Atmospheric tau neutrinos in a multikiloton liquid argon detector
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Conrad, Janet et al. “Atmospheric tau neutrinos in a multikiloton
liquid argon detector.” Physical Review D 82.9 (2010): 093012.© 2010
The American Physical Society.
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http://dx.doi.org/10.1103/PhysRevD.82.093012
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Atmospheric tau neutrinos in a multikiloton liquid argon detector
Janet Conrad,1Andre´ de Gouveˆa,2Shashank Shalgar,2and Joshua Spitz3 1Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Department of Physics and Astronomy, Northwestern University, Illinois 60208-3112, USA
3Department of Physics, Yale University, New Haven, Connecticut 06520, USA
(Received 24 August 2010; published 16 November 2010)
An ultralarge liquid argon time projection chamber based neutrino detector will have the uncommon ability to detect atmospheric = events. This paper discusses the most promising modes for identifying
charged current = , and shows that, with simple kinematic cuts,30 þ interactions can be
isolated in a 100 kt yr exposure, with greater than 4 significance. This sample is sufficient to perform flux-averaged total cross-section and cross-section shape parametrization measurements—the first steps toward using = to search for physics beyond the standard model.
DOI:10.1103/PhysRevD.82.093012 PACS numbers: 14.60.Pq
I. INTRODUCTION
Of all observed standard model particles, we have the least direct experimental knowledge of the tau neutrino, = .1A high statistics, dedicated experiment sensitive to
= charged current (CC) interactions has never been
performed and would add significantly to our understand-ing of electroweak interactions and be sensitive to certain hard-to-get manifestations of new physics [1]. Indeed, any opportunity to collect a significant sample of CC =
interactions and simply measure the cross section and perform basic tests of standard model predictions would qualitatively improve our knowledge of the third neutrino weak eigenstate.
The path to the observation of the was long, not
unlike that of the electron neutrino, e, and the muon
neutrino, . The discovery of the tau-lepton in 1975 [2]
led to the assumption of a third neutrino, , the
weak-isospin partner of the third charged lepton, . Since then, indirect information on the has been collected from a
wide range of tau-decay analyses [3–9]. The fact that the is a state orthogonal to and e, for example, was first
indirectly revealed by the LEP experiments via precision measurements of the Z-boson width [10]. The direct ob-servation of CC = interactions is a very recent (21st
century) development. The first events were presented by the DONuT experiment in 2000 and published in 2001 [11]. To date, ten CC interactions have been observed,
nine by DONuT and one by OPERA [12,13].2DONuT was a short-baseline, emulsion-based experiment. The = s
were produced by a fixed target 800 GeV proton beam configuration, primarily through the decay of Ds mesons,
with the relevant branching ratio BðDs ! Þ ¼ ð6:6 0:6Þ% [16]. The and contributed about 3%
of the total neutrino flux.
An alternative method for producing/detecting =
relies on neutrino oscillations. Our current understanding of the neutrino oscillation data [17,18] indicates that neu-trinos produced as = s will oscillate mostly into
= s with an oscillation frequency related to the largest
(in magnitude) of the two independent mass-squared dif-ferences, jm213j 2 103 eV2. This is true as long as the oscillation length associated with the smallest mass-squared difference, m212 8 105eV2, is much longer
than the characteristic baseline of the experiment. The relevant mixing angle is consistent with maximal (sin2223 1) [17,18] so a detector placed at one of the
oscillation maxima and exposed to an originally =
beam provides an ideal setup for collecting a large sample of CC = interactions. In practice, the design of such an
experiment has been demonstrated to be challenging. A large oscillation phase demands baselines above (and, preferably, well above) 1000 km, as the tau production threshold requires = s with laboratory energies above
3.5 GeV. To date, it has not been possible to produce a beam with an experimentally significant neutrino flux at distances beyond about 1000 km [19,20]. The OPERA experiment [21,22], a 1.25 kt emulsion-based detector, is aimed at directly observing CC events in a long baseline
beam. Unfortunately, the L=E 700 km=20 GeV factor does not allow for the collection of a large data sample. As of this writing, one candidate event has been observed
[13], with 10.4 events expected after five years of running at design luminosity [21].
Emulsion detectors provide the strongest resolving power for CC = interactions. Such detectors isolate
the events through the observation of a ‘‘kink’’ from the short-lived tau decay. However, automatic scanning of the emulsion is a time-intensive process which cannot proceed in real time. An alternative method, with real-time, fast event reconstruction using drift chambers was employed by the NOMAD experiment in an oscillation search [23]. No interactions were observed as the accessible m2
range was outside of what we now know is allowed. Liquid argon time projection chamber (LArTPC) detectors have 1
The distinction between and is made now in order to
avoid ambiguity later in the paper.
2This is dwarfed by, for example, the world’s growing sample
of reconstructed top quark events, which currently consists of well over 1000 events [14,15].
been proposed for = event searches, but have yet to be
specifically employed for this purpose [1]. Very recently, the ICARUS T-600 neutrino detector started operating in Gran Sasso. The ICARUS T-600 is a 600 ton LArTPC exposed, like OPERA, to the CNGS beam [24,25]. Although the experiment’s main goal is to observe
disappearance, ICARUS is also equipped to observe a number of CC interactions [26]. Unfortunately, the
expected event sample is too small to allow one to perform a cross-section measurement. In both the NOMAD and ICARUS experiments, the beam direction is used to search for evidence of missing transverse momentum consistent with tau production and decay.
The proposed 20 kt LArTPC at the Deep Underground Science and Engineering Laboratory (DUSEL) opens a new opportunity to collect a significant sample of =
events. Although the detector will be significantly larger than OPERA, the combination of longer baseline and significantly lower beam energy leads to anywhere from 0.2 to 4.0 expected CC beam-oscillated
events=MW 107 s=kt, depending on the (as-yet-undecided) beam tune [27].3 However, as a deep under-ground detector, this experiment will be sensitive to atmos-pheric neutrino interactions. A natural sample of high-energy, earth-diameter-as-baseline oscillations has the drawback of having no clear beam direction. In this paper, however, we show that this problem can be overcome so that a significant number of atmospheric = events can
be identified. We present a discussion of the capability of þ cross-section measurements as an example of the
physics potential of this signal.
The idea of a search for atmospheric = appearance
has been pursued before. The 22.5 kt (fiducial) Super-Kamiokande detector [28] results disfavor the no =
appearance hypothesis at the 2:4 level. However, this analysis was hampered by the lack of precision track reconstruction and particle identification inherent to Cherenkov-based detectors. A multikiloton LArTPC, on the other hand, will provide well-reconstructed events which can be used to isolate the = interaction signal
in a very convincing way, as we present below. We note that the authors of [29–31] have also considered the pos-sibility of studying atmospheric = using the Ice Cube
Deep Core Array and a LArTPC (with magnetic calorime-ter), respectively. The physics issues involved in the cal-culation of the = cross section at high energies
relevant to Ice Cube Deep Core Array–like experiments have recently been discussed in the literature [32].
This paper is organized as follows. In Sec.II, we discuss the ‘‘production’’ of = via atmospheric neutrino
oscil-lations and review the cross section and kinematics of CC
= interactions. In Sec.III, we present a brief overview
of LArTPC technology and details of our CC = event
simulation and the relevant CC and neutral current (NC) atmospheric neutrino-induced backgrounds. In Secs.IV,V, and VI, we discuss the search for CC = events via
statistical inference in various tau-decay modes, and offer some concluding remarks in Sec.VII.
II. ATMOSPHERIC TAU NEUTRINOS: PRODUCTION AND DETECTION
In order to understand an ultralarge LArTPC’s ability to detect = , it is important to know the properties of the
atmospheric = ‘‘beam’’ and the standard model
ex-pectation for the CC N ! X cross section, where N is a
nucleon and X is any hadronic final state. Both issues are discussed in this section.
A. The atmospheric= flux
Most atmospheric neutrinos are a result of pion decays (with a subleading kaon component), with the pions pro-duced when cosmic rays interact with the Earth’s atmo-sphere several kilometers above sea level. One naively expects a = to e= e production ratio close to 2
with virtually zero = s.4
Figure 1 depicts the flux of , , e, and e as a
function of the neutrino energy, for coszenith¼ 1 (left)
and coszenith¼ 0 (right), where coszenithis the cosine of
the zenith angle,5 according to [35]. Figure2depicts the fluxes as a function of zenith angle for E ¼ 5 GeV (left) and E ¼ 30 GeV (right). The uncertainty on the absolute normalization of the atmospheric neutrino fluxes is esti-mated to be around 20%, while the energy and zenith angle dependencies (shapes) are known to within 5% [36,37].
Between production and detection (while the neutrinos traverse a distance L), neutrinos oscillate. The relevant vacuum oscillation phases are
ij¼jm 2 ijjL 4E ¼ 7:8 jm2ijj 2:4 103 eV2 5 GeV E L 12 756 km ; (1) where 12756 km is the maximum diameter of the Earth. 13can be of order one for atmospheric neutrinos as long as L is not much smaller than the Earth’s radius. For coszenith¼ 0, L pffiffiffiffiffiffiffiffiffiffiffiffi2Rh 440 km (R is the Earth’s
radius and h 15 km is the average height above sea level
3We do not speculate on the possibility of LBNE-beam-based
= detection as it is extremely dependent on the largely
undecided beam parameters (e.g., beam energy spectrum).
4
A very small = component to the parent atmospheric
neutrino flux is expected from, for example, charm production. This addition is both very small and of higher energy than the atmospheric neutrinos considered here, and will be neglected henceforth [33,34].
5cos
zenith¼ þ1 corresponds to neutrinos coming from above
and coszenith¼ 1 to neutrinos coming from the antipodal
where neutrinos are produced), and 13 0:3 for 5 GeV
neutrinos. 12is always small unless the neutrino energies
are below 1 GeV; 12< 0:35 for neutrino energies above
3.5 GeV (the CC = production threshold) using
m2
12¼ 7:6 105 eV2. In summary, the oscillated
= flux above tau threshold comes from negative
coszenith and from the dominant ‘‘atmospheric’’
oscilla-tion frequency, proporoscilla-tional tojm213j.
The relevant oscillation probabilities are, ignoring mat-ter effects,
P cos213sin2223sin213 sin213; (2)
Pe sin223sin2213sin213< 0:09sin213; (3)
making use of the upper bound on 13from [18]. Figure3
depicts Pe (left) and P (right) as a function of the
neutrino energy with L ¼ 8000 km ( coszenith¼ 0:63)
for different values of 13 and assuming that the neutrino
mass hierarchy is normal (m213> 0). Note that the
sim-plifying approximations, allowing us to write Eqs. (2) and (3) above, were not made in generating Fig. 3, and that matter effects were properly taken into account. The PREM density profile was used to model the density of the Earth [38]. We safely conclude, further remembering
FIG. 2 (color online). Atmospheric neutrino flux as a function of coszenithfor E ¼ 5 GeV (left) and 30 GeV (right).
FIG. 1 (color online). Atmospheric neutrino flux as a function of the neutrino energy, for coszenith¼ 1 (left) and 0 (right).
FIG. 3 (color online). Pðe! Þ (left) and Pð! Þ (right) with L ¼ 8000 km for sin213¼ 0:005 (solid line) and 0.01 (dashed
that the = flux is larger than the e= e flux, that the
majority ( > 90%) of the = atmospheric neutrino flux
at energies above a few GeV comes from ! ( !
) oscillations. For large values of 13 and a normal
(inverted) mass hierarchy, there is a small but potentially significant fraction of ( ) from e ( e) oscillations.
Figure 4 depicts the atmospheric = flux at the
detector site as a function of energy (left) and zenith angle (right), for a fixed zenith angle and energy, respectively. We use the current best fit values of the neutrino oscil-lation parameters—m212¼ 7:6 105 eV2, m213 ¼
2:4 103 eV2, sin2
12¼ 0:31, and sin223 ¼ 0:5
[39–42]—and assume sin213¼ 0 and a normal neutrino
mass hierarchy. Prominent oscillatory features are clear in both panels of Fig. 4. In summary, = s arrive at the
detector mostly from ‘‘below’’ and are overwhelmingly low energy. Also, we expect most of the CC = initiated
events to occur close to tau production threshold. B. TheN ! X cross section
In the energy region of interest, CC = interactions
are well described as if the s were scattering mostly off
of nucleons. The kinematics of n ! p (or p !
þn) dictate that the minimum neutrino energy in the rest frame of the target nucleon is
Emin¼ m 1 þ m 2mN ¼ 3:46 GeV; (4)
where m is the tau-lepton mass and mN is the nucleon
mass, and assuming that the neutron and proton masses are the same.
Similar to CC e= e and = scattering, CC =
scattering receives contributions from a variety of pro-cesses. At low energies, quasielastic scattering n !
p ( p ! þn) dominates, while at high energies the
deep-inelastic scattering contribution is largest. At inter-mediate energies, it is expected that resonance production and other nonperturbative QCD phenomena dominate. The heavy tau mass (m¼ 1:777 GeV) shifts the regions
where the different contributions dominate towards higher energies. For example, the production of a resonance requires E * 4 GeV for CC scattering, as opposed to E * 0:44 GeV in the case of CC scattering. For CC scattering in the region of interest, Emin< E&
20 GeV, the three different contributions are similar. Quasielastic scattering is expected to dominate very close to threshold while deep-inelastic scattering is dominant above 10 GeV or so [43].
We will not discuss the challenges associated with com-puting the CC = cross section. Instead, we will
com-pare different results in the literature in order to illustrate the uncertainty of the situation. While a significant im-provement is expected in the near future from upcoming experimental data on = and e= e scattering, a large
uncertainty will remain in the = sector until more data
become available.
FIG. 4 (color online). Atmospheric and fluxes from oscillations as a function of neutrino energy (left) and cosine of the zenith
angle coszenith(right). In the left panel, the zenith angle is fixed at coszenith¼ 0:4, while in the right panel the energy is fixed at
E ¼ 5 GeV. We assume a normal neutrino mass hierarchy and 13¼ 0.
TABLE I. The expected number of CC = events=100 kt yr on an isoscalar target as
predicted by various cross-section models. The Nuance prediction for interactions on an argon target is also shown.
Model events events Total
NuTeV [44] 56.9 24.9 81.7
Kretzer and Reno [45] 37.7 17.5 55.2 Hagiwara, Mawatari, and Yokoya [46] 33.7 18.5 52.3 Paschos and Yu [43] 65.2 29.6 94.8
TableIcontains the expected number of atmospheric CC = events=100 kt yr from various cross-section
com-putations found in the literature [43–46] and the Nuance [47] prediction. The NuTeV collaboration has extracted Fe structure functions from the -Fe and -Fe deep-inelastic differential cross sections using its high-energy sign se-lected beam [44]. We compare the event rate from this data with those obtained from other cross-section models. The calculations done by Paschos and Yu [43] use leading order, whereas Kretzer and Reno [45] and Hagiwara, Mawatari, and Yokoya [46] use next to leading order structure functions to calculate the total cross section. The Kretzer and Reno model takes into account charm production, tau threshold, and target mass effects. The Hagiwara, Mawatari, and Yokoya model accounts for the effect of polarization on the deep-inelastic scattering cross section, unlike other models. All of these effects are only important in the low-energy region, however. The signifi-cant discrepancy in the high-energy region points to the lack of data presently available. Figure5depicts different predictions for the CC cross section at neutrino energies
below 30 GeV, where we expect the vast majority of events to occur. We bring attention to the fact that the different computations in the literature find different effective thresholds and that the shape of the rise in the cross section for energies close to threshold also changes from one estimate to the other. We should note that the Monte Carlo model used by Super-Kamiokande [28] has a cross section very close to that of Nuance, the neutrino event generator used in this paper and discussed later.
In an attempt to quantify these differences, we simply parametrize the cross section using
ðEÞ E ¼ ð1 expða ffiffiffiffiffiffiffiffiffiffiffiffiffi E b p ÞÞ 1038cm2 GeV ; (5)
where the parameter b fixes the production threshold value in the lab frame and the parameter a fixes the rate of increase near the threshold. The energy E and parameter b are in GeV and the parameter a is unitless. We find that this parametrization provides an excellent fit to the curves shown in Fig.5. The best fit values for these parameters are tabulated in TableII. Later, we calculate the experimental sensitivity to these parameters, assuming a =
measure-ment consistent with our Monte Carlo expectation. III. EXPERIMENTAL SETUP AND
EVENT SIMULATION A. Liquid argon time projection
chamber technology
The LAR20 detector provides a typical design for an ultralarge LArTPC [48]. We assume a 100 kt yr exposure for our event rate calculations, a modest estimate with the proposed 17 kt fiducial volume design and >10 years of data taking. Three wire planes, each with 3 mm wire spacing and 2 MHz sampling, will be instrumented. This granularity is insufficient to directly reconstruct the tau-decay kink and so the analysis presented here relies on indirect methods of isolating CC = interactions. The
detector’s active volume will be 15 15 34 m3, featur-ing multiple field cages with voltages of 500 V=cm (cor-responding to a drift velocity of 1:5 mm=s). Modest shielding is required for such a large detector so that the atmospheric neutrino events are not masked by and/or confused with cosmic ray tracks and interactions. LAR20 is proposed for the 800 ft level of DUSEL, which provides more than enough shielding for this analysis. Although a magnetized LArTPC has been demonstrated to work [49], the current LAR20 design does not include this feature. It should be noted that a magnetic field would greatly en-hance the analysis described here, allowing for possible
and separation and finer energy resolution, among other
things.
The spatial resolution for reconstructed tracks in the detector is at the millimeter scale in the drift and wire directions. A particle’s energy can be reconstructed by adding up all of the charge collected along a stopping track. In the case that the particle is identified with some confidence, measuring the distance of range out and/or
FIG. 5 (color online). The CC cross section for an isoscalar
target calculated according to different models: Paschos and Yu (long-dashed line), Kretzer and Reno (solid line), and Hagiwara, Mawatari, and Yokoya (short-dashed line). The Nuance (dotted line) cross-section prediction for an argon target is also shown.
TABLE II. The best fit parametrization for the various CC
cross-section models. See Eq. (5) for definition of a and b.
Model a b
NuTeV [44] 0.085 3.9 Kretzer and Reno [45] 0.080 5.6 Hagiwara, Mawatari, and Yokoya [46] 0.089 6.7 Paschos and Yu [43] 0.105 4.1 Nuance [47] 0.089 4.7
multiple scattering [50] can also be used to reconstruct the energy of the particle. These techniques can be used si-multaneously to measure the energy more precisely. Although the actual energy resolution is dependent on the particle’s energy and identity, the energy resolution for LArTPCs is usually quoted at the few percent level [51]. An example of data-based LArTPC neutrino event reconstruction can be found in Ref. [52]. In this analysis, we consider energy resolutions of 0% and 15%, recon-structed zenith angle resolutions of 0and 10, and 100% charged particle identification efficiency.
Although precise energy/angular resolution is not par-ticularly vital to this measurement as demonstrated below, the identification of charged and neutral pions is. Especially at >1 GeV energies, separating a charged or neutral pion from a proton/electron/muon/kaon, is nearly 100% efficient with LArTPCs. Particle identification pro-ceeds in several ways. First, there is the combination of energy deposition per unit distance (dE=dx) and range. dE=dx itself can distinguish highly ionizing particles such as protons and kaons from minimum ionizing ( 2:1 MeV=cm in liquid argon) particles such as charged pions and muons with close to 100% efficiency [53]. High-energy electrons and gammas (usually from neutral pion decay) are identified confidently as they lose most of their energy via bremsstrahlung and eþ=e pair production, creating a well defined electromagnetic shower. The ex-perimentalist can also take advantage of the gamma’s 18 cm conversion length in liquid argon, often resulting in a discernible gap between the interaction vertex (gamma creation point) and the beginning of the shower.
Pions are separated from muons via hadronic multiple scattering (with hadronic interaction length of 84 cm), nuclear capture, and decay products. A particle that travels longer than a few hadronic interaction lengths without a secondary interaction can be identified as a muon. In the case that a negatively charged particle does not decay in flight, a () will capture on argon 100% (76%) of the time. Negatively charged pions and muons can be differ-entiated in this way as the nuclear capture products are significantly different in each case. The decay chains ( ! ! e) and ( ! e) can also be used to separate pions from muons.
The majority of atmospheric = interactions are high
Q2, deep-inelastic scattering events usually with large multiplicity and vertex activity. Such events can be difficult to fully reconstruct for Cherenkov-based experiments and detectors with weak spatial resolution. Disentangling long, energetic tracks (possibly overlapping rings in the case of a Cherenkov-based detector) is relatively simple for LArTPCs featuring three-dimensional imaging and milli-meter resolution in a homogeneous and fully active vol-ume. Even in the case of multiple 0 production and subsequent decays (0 ! ), gamma pair matching is straightforward with the three-dimensional imaging
capabilities of LArTPCs and the help of a reconstructed invariant 0 mass.
B. Neutrino event generation
The Nuance (version 3) neutrino event generator [47] has been employed to simulate all-flavor atmospheric neu-trino interactions on argon. The Nuance source code, origi-nally created for simulating the interactions of atmospheric neutrinos with water, has been modified slightly in order to properly simulate the neutrino-argon interaction and the propagation of the resulting hadrons through the argon nucleus. The reader is referred to the Nuance documenta-tion for detailed informadocumenta-tion on the various cross-secdocumenta-tion and nuclear process models used in the program. Modeling the energy and angular distributions of the products of intranuclear collisions is difficult as there are many types of interactions and little data. In Nuance, hadrons are stepped through an argon nucleus with measured radially dependent density distribution and Fermi momentum. Some relevant argon-specific parameters are listed in Table III. The pion-nucleon and nucleon-nucleon cross sections and angular distributions are largely based on HERA data [54]. The understanding of the cross sections and angular distributions of relevant processes such as pion absorption, charge exchange, and elastic and inelastic scat-tering within the argon nucleus will be greatly improved by the ArgoNeuT [55], MicroBooNE [56], and ICARUS T-600 [24] experiments in the near future. These experiments will also improve our knowledge of the neutrino-on-argon cross sections themselves. Similarly, MINERA [57] will greatly enhance our knowledge of cross sections and intra-nuclear interactions using multiple intra-nuclear targets in the near future. The authors also look forward to a full intra-nuclear cascade simulation from the GENIE collaboration [58], featuring the simulation of ‘‘all (intranuclear) reac-tions on all nuclei.’’
Of special relevance to this paper, Nuance decays tau-leptons with the TAUOLA (version 2.6) package [59]. In CC quasielastic and deep-inelastic = interactions, the
polarization of the tau is calculated using the appropriate form factors [60]. The tau is considered completely polar-ized in resonant interactions, where the form factors are usually ambiguous and/or difficult to calculate [47].
TABLE III. Some relevant parameters in the simulation of neutrino interactions on (liquid) argon.
Liquid argon Nucleon binding energy¼ 29:5 MeV Fermi momentumðpÞ ¼ 242 MeV Fermi momentumðnÞ ¼ 259 MeV
Density¼ 1:396 g=cm3 Nuclear density ðrÞ ¼ 0 1þeðrcÞ=z c ¼ 3:53 fm z ¼ 0:542 fm
IV. HADRONIC TAU DECAYS, INCLUSIVE Identifying a = on an event-by-event basis will be
extremely difficult for a detector unable to resolve the kink from the tau decay, occurring only a fraction of a millime-ter from the event vertex for the most relevant atmospheric neutrino energies. However, statistically inferring the pres-ence of CC = interactions in a capable detector is
possible by analyzing event kinematics.
The tau decays to one or more hadrons and a neutrino about 65% of the time, with the branching ratios of the various channels well known. For convenience, we tabulate the relevant decay modes in TableIV. Looking for exclu-sive hadronic final states may assist in confirming the = appearance hypothesis. However, an exclusive
analysis (requiring a specific pion final state) is compli-cated by an increased dependence on the simulation of the relatively uncertain final-state interaction processes. We briefly consider the exclusive channels in the following section. In this section, we consider both inclusive pionic decays of and together. Note that there is no reason
that kaonic decays, compromising only about 3% of the total hadronic channel, cannot be included in this sample. However, we do not consider them for simplicity and because of their negligible effect on the analysis.
The largest background to = detection via
hadronic-channel-inclusive pion decay kinematics is the atmos-pheric neutrino NC interaction involving the excitation(s) and then subsequent decay(s) of a nuclear resonance to a pion and a nucleon (with a small pion contribution from elsewhere, such as NC coherent production). CC =
and e= e events are considered a negligible background
for = detection via the hadronic channels as the
effi-ciency of GeV-scale electron and muon identification is near 100% for LArTPC-based neutrino detectors [53]. Separation of the CC and NC channels is critical to the detector’s search for e= e appearance in the
accelerator-based part of the experiment.
Pions originating from neutrino-induced nuclear reso-nance decays (and elsewhere) and pions from tau decay form considerably different kinematic distributions. Variables such as visible energy, average energy per pion,
angle between the highest-energy pions, angle between the highest-energy pion and the (reconstructed) initial neutrino angle, energy of the highest-energy pion, invariant mass of the pionic system, and more are all useful, correlated, observables in differentiating pions originating from = events and pions from the NC background.
For a 100 kt yr exposure, 77.2 CC þ events are expected, based on the previously discussed oscillated at-mospheric neutrino flux and the Nuance cross-section pre-dictions. Of these, 46.3 events feature at least one charged pion from tau decay. CC = events involving a charged
lepton from the tau decay are not considered here, even if a non-tau-decay pion escapes the nucleus. Visible energy (Evis), cos(reconstructed zenith angle) ( cosðzenithðrec:ÞÞ),
and energy of the highest-energy neutral or charged pion (E") have been found to be the most useful variables in
differentiating signal from background. These variables also happen to be among the simplest to measure experi-mentally. We initially consider events with at least one visible charged pion. Note that the pions in the CC þ
sample are not all necessarily from the tau decay (e.g.,
they might be resonant-induced), although a tau decay to at least one charged pion is required to enter the sample.
Events with cosðzenithðrec:ÞÞ < 0:2 and one or more charged pions enter the þ candidate sample.
Reconstructed zenith angle is defined assuming full knowl-edge of all final-state and tau-daughter non-neutrino/neutron particles. The reconstructed zenith angle cut is applied to reduce the downward-going NC background as few =
events are expected in this region. The cut is stricter than the usual cosðzenithðrec:ÞÞ < 0:0 cut in order to compensate for the limitations of reconstructed angle resolution in differ-entiating upward- from downward-going events.
With a 3.5 GeV threshold, CC = interactions
gen-erally occur at higher energies than the other possible atmospheric neutrino interactions. Visible energy is de-fined as the sum of the energy of all primary particles and tau-decay products minus the energy contribution of any and all neutrinos and neutrons. Figure 6 shows the visible energy of our sample, separated into NC, CC þ
, and total after simulating atmospheric neutrinos with
energy 3 < E< 30 GeV. Requiring Evis> 6:0 GeV is
found to be effective in isolating the = events from
the NC background. The visible energy cut was chosen to improve signal-to-background, although a thorough opti-mization of this cut has not been performed. Reference [30] also found a 6–7 GeV visible energy cut useful for isolating atmospheric = events.
Figure 7 shows E" for each sample after the visible
energy cut. After further requiring E"> 1:5 GeV, we
are left with 73.4 total events over a background of 44.8 events, a 4:3 excess (with Poisson statistics only) assuming experimental data that are consistent with the Monte Carlo expectation. This excess has been found to be largely insensitive to the effects of even modest energy and
TABLE IV. Branching ratios of selected decay modes [16]. decay mode Branching ratio
ee 17.8% 17.4% 11.1% K 0.69% 0 25.4%a ð 1hÞð 0h0Þ 62.6%b
aAll but a small fraction (0.3%) of this branching ratio is
mediated by a resonance.
b
reconstructed angle resolutions. Applying a Gaussian smear (with a 15% sigma) to each event’s Evis and E"
and a Gaussian smear (with a 10sigma) to cosðzenithðrec:ÞÞ (all smears together) left the excess at 3:9. Similarly, varying each cut individually by 15%, while leaving the other two cuts at their nominal values, dropped the excess down to 4:2 at worst. For completeness, we also consider the low end and high end of the rates predictions. Scaling the Nuance prediction’s excess to match the Hagiwara, Mawatari, and Yokoya (low-end) and Paschos and Yu (high-end) rates changes the excess significance to 2:9 and 5:2, respectively.
The background event rates quoted above rely on the understanding of the NC cross sections in the few to
30 GeV energy range and final-state interactions. Fortunately, experiments such as those mentioned in Sec.III Bwill soon improve our knowledge of these pro-cesses. The Nuance event generator represents our best estimate of the NC background and we employ it with the understanding that the ‘‘real’’ background (and signal) may be substantially different from that which is predicted. The apparent flexibility of the resolution/cuts described above demonstrates that the sensitivity quoted will only minimally depend on the modeling of NC cross sections and final-state interactions. Moreover, a strong excess re-mains even in the case that Nuance severely underpredicts the background. Arbitrarily increasing the background that passes all cuts by 50% (while leaving the signal at its nominal level) leaves the excess at 3:5. Furthermore, the background can be measured directly using downward-going events, where no / appearance
events are expected (see Fig. 4, right) with the energy and zenith angle dependencies of the flux known to within 5%. After imposing the three cuts previously discussed, 48.9 downward-going [ cosðzenithðrec:ÞÞ > 0:2] NC events are expected, with less than 0.1 events coming from CC = . These events provide an in situ background
mea-surement after extrapolating the flux from downward- to upward-going.
This analysis would benefit from a neural network and/ or likelihood analysis involving the many correlated kine-matic variables useful for discriminating CC = from
the NC background. Although a complicated multilayer approach to inferring atmospheric = appearance could
be utilized to improve sensitivity, we have shown that simple observables (and a finely grained and efficient detector with particle identification capabilities) are all that is necessary for this measurement.
V. HADRONIC TAU DECAYS, EXCLUSIVE The inclusive hadronic decays are broken up into their constituent exclusive channels in Table V. The three cuts discussed above [Evis> 6:0 GeV, E"> 1:5 GeV, and
cosðzenithðrec:ÞÞ < 0:2] are used to arrive at the expected
number of events. The categorization of the inclusive channels cannot simply be made according to the expected tau-decay products and branching ratios as at least one non-tau-decay pion appears in 68% of the CC = events
simulated. For example, requiring the invariant mass of a charged and neutral pion pair to match the meson peak, in an effort to isolate the most likely decay channel ( ! 0, with a branching ratio of 25.4%), is complicated
by these non-tau-decay pions. Figure8shows the invariant mass of the highest-energy charged and neutral pion in events with >0 charged pions, 1 neutral pion, Evis>
6:0 GeV, and cosðzenithðrec:ÞÞ < 0:2. Although a clear
peak is visible, signal events often do not reconstruct well to the mass. Furthermore, the NC background contains a significant amount of resonances, a consequence of
FIG. 6. The visible energy for NC interactions with at least one final-state charged pion and CC þ interactions with the tau
decaying to at least one charged pion. Events with Evis>
6:0 GeV enter the final sample.
FIG. 7. The energy of the highest-energy pion, neutral or charged, for NC interactions with at least one final-state charged pion and CC þ interactions with the tau decaying to at
least one charged pion. Non-tau-decay pions (e.g., resonant-induced) are also considered in the CC þ sample.
vector meson dominance. Requiring the highest-energy charged and neutral pion invariant mass to be greater than 500 MeV along with the same three cuts on events with a single neutral pion and one or more charged pions only negligibly increases the sensitivity.
Although the actual sensitivity to = appearance
cannot be improved via an exclusive analysis, such an analysis can help to confirm that a possible excess is in fact from = interactions rather than nonstandard
neu-trino interactions. That is, seeing the expected excess in each charged/neutral pion category consistent with tau decay (and the expected non-tau-decay-pion contribution) can rule out nonstandard neutrino interactions as the source of an excess.
It is worth noting that atmospheric CC = events
with a kaon in the final state (i.e., ! K) should not be considered a background for the proton decay channel p ! Kþ. An argon-bound proton’s decay kaon is expected to have a momentum of less than 500 MeV=c as it exits the nucleus, taking into account the effects of kaon rescattering (with or without an argon spectral function) [61]. Conservatively requiring the kaon’s momentum to be
<500 MeV=c, less than 0.05 CC = ( ! K)
events=100 kt yr are expected.
VI. LEPTONIC TAU DECAYS
The tau decays to a charged lepton and two neutrinos with a branching ratio of about 35%. Accelerator-based = appearance experiments without the ability to see
the decay kink in such events can infer the presence of a = interaction by searching for missing transverse
en-ergy (carried away by the two unseen neutrinos). This missing transverse energy is absent for background CC = =e= e events which do not feature final-state
neu-trinos. However, an atmospheric appearance search is
not afforded the luxury of a known beam direction and a missing transverse energy search is therefore difficult.
Compared to the inclusive hadronic modes discussed above, the CC = leptonic channels have a higher
background and smaller signal. The leptonic channel’s background (CC = =e= e) cross section is almost 3
times higher than its NC counterpart and the signal tau decays to a charged lepton about half as often as it does to one or more hadrons. Furthermore, there are fewer cuts available to separate background from signal. The power-ful visible energy cut used for the inclusive hadronic final states above is rendered mostly useless for the leptonic case as the CC = ’s unseen neutrino daughters push the
event’s visible energy down, overlapping more with the background CC = =e= e visible energy. Requiring
cosðzenithðrec:ÞÞ < 0:2 and Evis> 3:0 GeV, we find 20 CC
þ events with an expected background of 610 CC
þ þ eþ eevents (see Fig.9). Cuts involving the
charged lepton’s transverse momentum and direction, both with respect to the reconstructed neutrino direction, have been found to be largely ineffective. We find the leptonic channel an unlikely source for atmospheric =
investigation.
TABLE V. The expected number of CC þ and NC
background events=100 kt yr after cuts for hadronic tau-decay channels categorized by number of charged and neutral pions.
Exclusive channel (’s) Total/ Background Excess significance () 1 charged, 0 neutral 2:3=1:6 0.6 1 charged, 1 neutral 5:9=3:2 1.5 1 charged, >1 neutral 6:9=3:5 1.8 >1 charged, 0 neutral 11:5=7:6 1.4 >1 charged, 1 neutral 21:5=14:1 2.0 >1 charged, >1 neutral 25:3=14:8 2.7 Total 73:4=44:8 4.3
FIG. 8. The invariant mass of the highest-energy charged and neutral pion for NC interactions and CC þ interactions
with one neutral pion and at least one charged pion. Non-tau-decay pions are also considered in the CC þ sample.
FIG. 9. The visible energy distribution of charged leptons from signal CC þ and background CC þ þ eþ e
VII. CONCLUSIONS
The = is the least well understood observed
stan-dard model particle with only ten events ever identified. Simply measuring the cross section and testing the stan-dard model prediction, after obtaining a sizable sample of events, will improve our understanding of this elusive particle. The prospect of measuring the atmospheric neu-trino mixing parameters from a ! ( ! )
ap-pearance experiment, however imprecisely, rather than a ! = ( ! = ) disappearance experiment would
also be a strong corroboration of the three neutrino mixing model in general.
Along with offering an attractive detector for high- and low-energy accelerator-based neutrino oscillation experi-ments, atmospheric = disappearance measurements,
proton decay searches, and sensitivity to supernova burst and diffuse neutrinos, among other things, a kiloton-scale LArTPC will also be capable of observing a significant number of atmospheric = appearance events. Contrary
to naive expectations, we find that the most promising way of detecting atmospheric = s is through the study of the
tau hadronic decay modes as it is difficult to separate tau-decay leptons and leptons coming from CC e= e and
= interactions. After simple cuts on visible energy,
reconstructed zenith angle, and energy of the highest-energy pion in atmospheric neutrino events with no charged lepton, 28.5 tau neutrino events over a background of 44.8 events are expected from a 100 kt yr exposure, corresponding to a 4:3 excess signal with Poisson statis-tics only. Although the detection of such events might be considered ‘‘indirect’’, the expected signal-to-background ratio over most of the kinematic range (after cuts) is >0:5 and even >1 at high energies (see Fig.7). Furthermore, by studying the exclusive decay channels categorized by num-ber of charged/neutrino pions, the possibility of an excess in the inclusive analysis being a result of some form of nonstandard interaction, rather than = production, can
be disfavored.
Given a measurement consistent with the simulated sample, the expected statistical-error-only sensitivities to the CC cross-section parametrization and the
flux-averaged total CC þ cross section (6 < Evis<
30 GeV) from a 100 kt yr exposure are shown in Figs. 10 and 11 along with the predictions of various cross-section models. Such measurements would provide
basic tests of the standard model and vastly improve our knowledge of the elusive third neutrino weak eigenstate.
ACKNOWLEDGMENTS
We would like to thank Bonnie Fleming, Mitchell Soderberg, Chris Walter, and Geralyn Zeller for helpful discussions. We thank the hospitality of Fermilab where a lot of this work was carried out. AdG and SS are sponsored in part by the U.S. Department of Energy Contract No. DE-FG02-91ER40684. J. C. is sponsored in part by the National Science Foundation Grant No. PHY0847843.
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